Question

The angles in a right-angled isosceles triangle are:
$
  {\text{A}}{\text{. 90}}^\circ ,30^\circ ,60^\circ \\
  {\text{B}}{\text{. 90}}^\circ ,20^\circ ,70^\circ \\
  {\text{C}}{\text{. 90}}^\circ ,40^\circ ,50^\circ \\
  {\text{D}}{\text{. 90}}^\circ ,45^\circ ,45^\circ \\
$

Answer 1

Hint: According to properties of triangles, the sum of angles in a triangle is 180$^\circ $. Since it is a right angles triangle, one angle is 90$^\circ $. The other two angles are equal because it is isosceles.

Complete step-by-step answer:

Given Data, it is a right-angled isosceles triangle.

In an isosceles triangle two sides are equal.
Therefore, the angles opposite to both the respective sides are equal.
Let that angle be x.
It is a right angled triangle. Hence one of the angle is 90°.
We know that the sum of angles in a triangle is 180°.
So, 90° + 2x = 180°
        ⟹2x = 90°
         ⟹x = 45°

Each of the other angles is 45°.

Hence the angles in a right-angled isosceles triangle are 90°, 45° and 45°.
Option D is the correct answer.

Note: In order to solve this type of questions, the key is to remember that the sum of angles in a triangle is 180° and in a right-angled isosceles triangle one of the angles is 90° and the other two angles are equal. We correlate all these properties to determine the answer.